# Detecting Stems in Dense and Homogeneous Forest Using Single-Scan TLS

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## Abstract

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## 1. Introduction

## 2. Study Area and Data

^{2}and the distance between the nearest bamboo and the scanner was about 4.0 m. Plot B covers a ground area of about 120 m

^{2}and the distance between the front side and the LiDAR was about 5.0 m. The terrain surfaces in both plots are uneven and common in natural forests. There were 82 reference stems in Plot A and 84 in Plot B. The number of reference plants and relative stem map was recorded manually using Terrascan™ software (Terrasolid Ltd., Helsinki, Finland). To avoid false statistics in 3-D point clouds, we divided the plots into small sections; then the number and relative positions were recorded successively. In terms of the undergrowth, stem density and topographic relief, Plot A and Plot B are quite typical. Although the areas of two plots are smaller than those in previous studies, the number of reference stems is sufficient compared to relevant studies [5,8,14,18].

**Figure 1.**Diagram of two plots. The side near the LiDAR position is defined as front and its opposite is defined as back. Circles indicate relative stem locations.

## 3. Methods

#### 3.1. Two-Scale Classification

#### 3.1.1. Multi-Scale Features of Vegetation Point Clouds

_{1}, λ

_{2}, λ

_{3}) (λ

_{1}≥ λ

_{2}≥ λ

_{3}) and three associated eigenvectors (e

_{1}, e

_{2}, e

_{3}) representing three orthotropic axes of the spatial distribution of local points [23]. The axial lengths are ${\delta}_{i}=\sqrt{{\lambda}_{i}}$ (i = 1,2,3). Three geometric features are defined to represent the shape of local point set distribution (Equation (1)). Each point is classified as linear (a

_{1D}), planar (a

_{2D}) or volumetric (a

_{3D}) according to the maximum value among a

_{1D}, a

_{2D}, and a

_{3D}[24].

Point clouds of stem (Height ≈ 80 cm, Radius ≈ 4 cm) | ||||||||||||

radius (cm) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

linear (%) | 52.24 | 6.62 | 4.06 | 2.82 | 16.23 | 88.44 | 91.13 | 93.47 | 95.91 | 98.41 | 99.94 | 100 |

planar (%) | 47.11 | 75.32 | 95.55 | 96.43 | 82.24 | 11.23 | 8.86 | 6.54 | 4.09 | 1.59 | 0.06 | 0 |

Volumetric (%) | 0.65 | 18.06 | 0.39 | 0.75 | 1.43 | 0.33 | 0.01 | 0 | 0 | 0 | 0 | 0 |

Branch | Foliage | Grass | Ground | |||||
---|---|---|---|---|---|---|---|---|

point number | 119 | 67,537 | 5996 | 7287 | ||||

classified points | ||||||||

dimensions (m) | 0.1/0.5 | 1.5/2.3 | 0.8/1.8 | 0.6/1.2 | ||||

radius (cm) | 4 | 12 | 4 | 12 | 4 | 12 | 4 | 12 |

linear (%) | 100 | 100 | 10.50 | 7.69 | 49.87 | 14.28 | 6.24 | 2.83 |

planar (%) | 0 | 0 | 11.49 | 13.27 | 16.84 | 5.85 | 84.29 | 97.17 |

volumetric (%) | 0 | 0 | 78.01 | 79.04 | 33.29 | 79.87 | 9.47 | 0 |

#### 3.1.2. Optimal Radius Selection

_{1}, r

_{u}] that contains candidate optimal radius is predefined. E values with radiuses in the given interval for each point are computed. Finally, for each point, the radius with minimal E is selected as the optimal radius. The pseudo code of the scale determination is presented in Algorithm 1. According to Equation (2), a smaller E value indicates that one of the feature values (i.e., a

_{1D}, a

_{2D}, a

_{3D}) is much greater than the other two [26], which can be used as an index to distinguish geometric feature.

Algorithm 1. Scale selection | ||

Input: Point clouds P; Given interval $[{r}_{1},{r}_{u}]$Output: radius set R | ||

for every point P_{i} ∈ P do | ||

for every radius r_{j} ∈ [r_{1}, r_{u}] do | ||

Find the neighboring points set s_{j} of p_{i} with ${r}_{j}$.Calculate geometric features according to Equation (1). Calculate and record the entropy function E _{j} according to Equation (2). | ||

end for | ||

The radius r_{min} with minimal E_{min} is selected as the optimal radius for ${p}_{i}$.Add r _{min} to R. | ||

end for |

#### 3.1.3. Candidate Stem Points Recognition

_{1}, r

_{2}] and [r

_{3}, r

_{4}] (r

_{1}< r

_{2}≤ r

_{3}< r

_{4}), corresponding to two scales, are introduced to find optimal radiuses for each point at different scales. A small increment of radius will improve the precision, but also increase the calculation load. It was set to 0.5 cm in both intervals to keep a balance between precision and computing time according to tests. By using the Algorithm 1, the optimal radiuses for each point at each scale are acquired. Then points will be classified into linear, planar or volumetric according to Equation (1) at both scales. Finally, stem points can be recognized by combining two-scale features. The main steps of classification are listed in Algorithm 2. The ranges of two intervals can be set according to the radius of trees. In our method, the lower bound (r

_{1}) of the first interval should be larger than the point spacing while its upper bound (r

_{2}) should be smaller than the max stem radius in the scene. As for the second interval, its lower bound (r

_{3}) should be no less than r

_{2}. Because a wider range of interval will increase the unnecessary computation, it is suitable to set the upper bound (r

_{4}) around double the value of r

_{3}according to trials

Algorithm 2. Two-scale classification | |

Input: Point clouds P; Given intervals [r_{1}, r_{2}] and [r_{3}, r_{4}]Output: Candidate stem point set P_{stem} | |

(1) Run Algorithm 1 with interval [r_{1}, r_{2}], get optimal radiuses for all points. | |

(2) Classify each point into linear, planar or volumetric according to Equation (1). | |

(3) Only “planar” points remain | |

(4) Run Algorithm 1 with interval [r_{3}, r_{4}], get optimal radiuses for remaining points. | |

(5) Classify these points into linear, planar or volumetric according to Equation (1). | |

(6) These “linear” points are recognized as candidate stem points P_{stem} |

#### 3.2. Clustering

_{e}will be considered as subordinates to the same cluster, otherwise they belong to two different clusters. Update the clusters until all points are assigned to a certain cluster. The number of points in each cluster is used to name cluster size, which is determined by the point spacing. Generally, stem clusters are much bigger than the residual non-stem clusters. Therefore, clusters with their size less than N

_{c}are excluded from the candidate stem clusters. N

_{c}can be specified according to the original point density. d

_{e}is the only parameter needed to be set in clustering and has a major influence on the cluster size. The aim of clustering is to group the “planar” points and therefore d

_{e}should be selected according to “planar” points’ density. Generally speaking, neighbors within the optimal radius of one point are considered to have similar properties. Therefore, in this method, the mean optimal radius of “planar” points at the first scale classification is used as d

_{e}adaptively.

#### 3.3. Merging Stem Clusters

_{ef}(a, b, c are parameters) of line ef, which is the projection of a stem on ouz plane, and it also can be expressed as a function of x and y (Equation (5)) while the relationship between x and y is linear (Equation (6)). If we eliminate y in Equation (6) by substituting Equation (5), line ef can be expressed as Equation (7). Then, the left hand side term of Equation (4) is substituted by the right hand side term of Equation (7). Finally, the relationship between x and z can be expressed as Equation (8). Furthermore, f

_{y}(z) can be expressed in the same way like ${f}_{x}(z)$.

_{x}, T

_{y}, T

_{z}) of stem (e.g., red line in Figure 3a) can be expressed as the derivative of Equation (3). It forms a simple stem model as shown in Equation (9). A

_{i}and B

_{i}are direction parameters.

_{stem}, two clusters are considered from the same stem. Figure 3b shows an example of the direction–growing algorithm. Two higher stem clusters have the same direction vector and height, but after the lower cluster grows up, the left cluster will be merged with the lower one according to the distance comparison. This merging process is summarized in Algorithm 3.

Algorithm 3. Merging of stem clusters | |||

Input: points clusters COutput: stems list Cs | |||

Initialize an empty list of Cs | |||

for every cluster c_{i} ∈ C do | |||

for every stem cs_{j} ∈ Cs do | |||

find the cluster c_{k} ∈ cs_{j} which is nearest to c_{i}calculate the direction vectors of c _{k} and c_{i} | |||

solve parameters of linear models in Equation (9) using two direction vectors | |||

growing of the seed point according to Equation (10) until it meets the higher cluster | |||

if distance (c_{k}, c_{i}) < d_{stem} then | |||

add c_{i} to cs_{j}; break; | |||

end if | |||

end for | |||

if c_{i} is not added to any cs_{j} ∈ Cs then | |||

create a new stem and add it to Cs | |||

end if | |||

end for |

## 4. Experiments and Results

_{c}, a parameter used in clustering, was set as 50, which means only a cluster’s bigger than 50 will be considered as a stem cluster. N

_{c}= 50 was determined based on tests in the plots and density of the raw points. The last parameter d

_{stem}depends on the minimum distance between neighboring stems and was set to 8 cm in two plots. Additionally, fallen bamboos on the ground can also be detected in two plots. Thus, any merged stem with its height, i.e., maximum height minus minimum height in the group, less than 30 cm will be excluded.

Original | First Scale Classified | Second Scale Classified | Clustering | Merging | |
---|---|---|---|---|---|

Plot A | 3,384,528 | 1,095,781 | 551,077 | 340,133 | 329,417 |

Plot B | 3,050,403 | 995,032 | 494,154 | 283,083 | 280,335 |

Reference Bamboos | Detected Culms | Type I Error | Type II Error | True Culms | Completeness | |
---|---|---|---|---|---|---|

A | 82 | 78 | 1 | 5 | 73 | 89% |

B | 84 | 79 | 2 | 6 | 73 | 86.9% |

Total | 166 | 157 | 3 | 11 | 146 | 88.0% |

## 5. Discussion

#### 5.1. Stem Points Identification and Type I Error

_{3}, r

_{4}]) becomes much bigger. In fact, if stem diameters are much bigger, the stem density in forests as well as the shadowing effect may reduce. Therefore, classical cylinder fitting methods [8,13,15,16] may be feasible and fast for stem detection in these circumstances.

**Figure 5.**An example of two-scale classification: (

**a**) classification results at the first scale; and (

**b**) classification results at the second scale.

#### 5.2. Clusters Merging and Type II Error

**Figure 6.**(

**a**) Side view of Plot A: Bamboo on the hillside is inclined and stem clusters are fragmentized. (

**b**) Details of Plot B: Stems are clumped and some are seriously inclined.

_{stem}in the direction–growing process, they will be merged as one stem and thus cause errors in counting. In addition, if parts of stems cling together, the points from different stems will be grouped together in the clustering and lead to Type II errors directly. However, this kind of situation rarely happens.

**Figure 7.**Error types: (

**a**) Bamboos are too close to each other; (

**b**) two independent stems; (

**c**) mutual containment of two stems after growing; (

**d**) one stem (in red) contains part from the other one; and (

**e**) two stems are totally merged as one.

_{stem}is helpful in reducing the Type II error. For instance, three neighboring stems were recognized as one (magenta) in Figure 8a. In Figure 8b, by setting d

_{stem}= 5cm, one (red) of the three stems can be separated. The second method is to adopt a bigger N

_{c}to delete small stem clusters, because the directions of small clusters are often incorrect and affect the results. In Figure 8c, by setting N

_{c}= 80, three stems are separated correctly. However, changing parameters for eliminating some errors may affect the results of other stems. It is better to extract false stems first and then set specific parameters to achieve better results.

**Figure 8.**Error correction: (

**a**) Error connected results; (

**b**) results by setting d

_{stem}= 5cm; and (

**c**) merged results by setting N

_{c}= 80.

#### 5.3. Measuring Range and Quality Assessment

_{e}). The indictor is defined in Equation (12) where n is the number of contained clusters in each stem. D

_{i}(P

_{i,h}, P

_{i,1}) is the distance between P

_{i,h}and P

_{i,1}corresponding to the highest and lowest points of each cluster, respectively.

_{e}indicates a good stem quality. Table 5 summarizes the statistical results of H

_{e}in both plots. Only the correctly detected stems are analyzed. There are about 52% of all the stems with their heights higher than 4.0 m and 17 detected stems are more than 6.0 m high. However, 17.1% of detected stems are lower than 2.0 m, which indicates that only a small fraction (less than 20%) of a whole stem is detected. In general, the mean effective height is about 4.0 m.

H_{e} (m) | <2.0 | 2.0–3.0 | 3.0–4.0 | 4.0–5.0 | 5.0–6.0 | 6.0–7.0 | >7.0 | Sum |
---|---|---|---|---|---|---|---|---|

Plot A | 15 | 13 | 7 | 19 | 12 | 3 | 4 | 73 |

Plot B | 10 | 14 | 11 | 18 | 10 | 6 | 4 | 73 |

Total | 25 | 27 | 18 | 37 | 22 | 9 | 8 | 146 |

Percentage | 17.1% | 18.5% | 12.3% | 25.3% | 15.1% | 6.2% | 5.5% |

_{e}), the grid density (i.e., number of points in every 0.5 m along the distance) and the measuring range of Plot A are plotted in Figure 10. It can be found that the grid density dropped rapidly after the first row of bamboo stands. However, if there are no objects (e.g., foliage) shading the lasers, the point spacing within a small measuring range (e.g., 8 m in this paper) will change little, so the reason for a sharp decline in point number is shadowing. The bamboo in the front blocks much of the emitted lasers. In addition, the effective height (H

_{e}) tends to decrease as the measuring range increases in Figure 10. According to the trend line in Figure 10, when the distance is greater than 5.5 m, H

_{e}is more likely to be less than 3.0 m. However, if only the stems within 3.5 m along measuring range are evaluated, the mean effective height is 5.1 m (27 detected stems in total).

**Figure 10.**Point counts and H

_{e}change with distance in Plot A. The correlation coefficient between trend line and height data is 0.37.

_{2}) of the first interval is usually smaller than the stem radius (e.g., 4 cm in this paper), and thus to keep the geometry significance, sufficient points within the upper bound of a point are needed. In addition, a large point spacing of stem points will lead the stem cluster to be fragmentary and ignored during clustering process. Thus, the minimum point spacing of stem points is recommended to be a fifth of the stem radius empirically. The measuring range can be determined according to this criterion. Besides, a direct way is to run the detection algorithm on original point clouds first and we can get a relationship between distance and effective height, e.g., the trend line in Figure 10. Then the effective measuring range can be determined according to requirements, for example, if the detected stem height is expected to be no less than 3.0 m, the measuring range in Figure 10 should be less than 5.5 m.

^{2}). In this paper, if we use 5.5 m as an effective measuring range in each scan, it would probably need 105 scans to cover a whole hectare, while the distance between adjacent scanners may be approximate to twice the effective measuring range, e.g., 11 m. However, if a longer measuring range in each scan is set, e.g., 8 m, and the spacing between adjacent scanners is longer than 11 m but smaller than 16 m, e.g., 14 m, we may get better stem detection results with less scans (approximately 65) in one hectare by combining multi-scan detection results. However, further experiments are needed to explore the feasibility and potential problems in practice.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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## Share and Cite

**MDPI and ACS Style**

Xia, S.; Wang, C.; Pan, F.; Xi, X.; Zeng, H.; Liu, H.
Detecting Stems in Dense and Homogeneous Forest Using Single-Scan TLS. *Forests* **2015**, *6*, 3923-3945.
https://doi.org/10.3390/f6113923

**AMA Style**

Xia S, Wang C, Pan F, Xi X, Zeng H, Liu H.
Detecting Stems in Dense and Homogeneous Forest Using Single-Scan TLS. *Forests*. 2015; 6(11):3923-3945.
https://doi.org/10.3390/f6113923

**Chicago/Turabian Style**

Xia, Shaobo, Cheng Wang, Feifei Pan, Xiaohuan Xi, Hongcheng Zeng, and He Liu.
2015. "Detecting Stems in Dense and Homogeneous Forest Using Single-Scan TLS" *Forests* 6, no. 11: 3923-3945.
https://doi.org/10.3390/f6113923